he

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

פּוֹפּוּלָרִי אלגברה >

expand (6-\sqrt[4]{x/(13060694016)})^{19}

פתרון

expand

(6 - 4 \frac{x}{13060694016})^{19}

פתרון

6^{19} - \frac{6 ^{18} \cdot 19 4 x}{4 13060694016} + 6^{17} \cdot 171 (4 \frac{x}{13060694016})^{2} - 6^{16} \cdot 969 (4 \frac{x}{13060694016})^{3} + 139536 x - 69768 x 4 \frac{x}{13060694016} + \frac{2261 x x}{3888 6} - \frac{8398 x 4 x ^{3}}{4 1306069401 6 ^{3}} + \frac{2.74209 E 13 x ^{2}}{1306069401 6 ^{2}} - \frac{5585744406528 x ^{2} 4 \frac{x}{13060694016}}{1306069401 6 ^{2}} + \frac{3325608 6 x ^{2} x}{1306069401 6 ^{2}} - \frac{126948736512 x ^{2} 4 x ^{3}}{1306069401 6 ^{2} 4 1306069401 6 ^{3}} + \frac{14105415168 x ^{3}}{1306069401 6 ^{3}} - \frac{1265870592 x ^{3} 4 \frac{x}{13060694016}}{1306069401 6 ^{3}} + \frac{323 6 x ^{3} x}{1306069401 6 ^{3}} - \frac{5023296 x ^{3} 4 x ^{3}}{1306069401 6 ^{3} 4 1306069401 6 ^{3}} + \frac{209304 x ^{4}}{1306069401 6 ^{4}} - \frac{6156 x ^{4} 4 \frac{x}{13060694016}}{1306069401 6 ^{4}} + \frac{19 x ^{4} x}{1306069401 6 ^{4} 362797056} - \frac{x ^{4} ( 4 \frac{x}{13060694016} ) ^{3}}{1306069401 6 ^{4}}

צעדי פתרון

(6 - 4 \frac{x}{13060694016})^{19}

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

:הפעל את הבינום של ניוטון

a = 6, b = - 4 \frac{x}{13060694016}

= i = 0 \sum 19 (i 19) \cdot 6^{(19 - i)} (- 4 \frac{x}{13060694016})^{i}

הרחב את הסכום

= \frac{19 !}{0 ! ( 19 - 0 ) !} \cdot 6^{19} (- 4 \frac{x}{13060694016})^{0} + \frac{19 !}{1 ! ( 19 - 1 ) !} \cdot 6^{18} (- 4 \frac{x}{13060694016})^{1} + \frac{19 !}{2 ! ( 19 - 2 ) !} \cdot 6^{17} (- 4 \frac{x}{13060694016})^{2} + \frac{19 !}{3 ! ( 19 - 3 ) !} \cdot 6^{16} (- 4 \frac{x}{13060694016})^{3} + \frac{19 !}{4 ! ( 19 - 4 ) !} \cdot 6^{15} (- 4 \frac{x}{13060694016})^{4} + \frac{19 !}{5 ! ( 19 - 5 ) !} \cdot 6^{14} (- 4 \frac{x}{13060694016})^{5} + \frac{19 !}{6 ! ( 19 - 6 ) !} \cdot 6^{13} (- 4 \frac{x}{13060694016})^{6} + \frac{19 !}{7 ! ( 19 - 7 ) !} \cdot 6^{12} (- 4 \frac{x}{13060694016})^{7} + \frac{19 !}{8 ! ( 19 - 8 ) !} \cdot 6^{11} (- 4 \frac{x}{13060694016})^{8} + \frac{19 !}{9 ! ( 19 - 9 ) !} \cdot 6^{10} (- 4 \frac{x}{13060694016})^{9} + \frac{19 !}{10 ! ( 19 - 10 ) !} \cdot 6^{9} (- 4 \frac{x}{13060694016})^{10} + \frac{19 !}{11 ! ( 19 - 11 ) !} \cdot 6^{8} (- 4 \frac{x}{13060694016})^{11} + \frac{19 !}{12 ! ( 19 - 12 ) !} \cdot 6^{7} (- 4 \frac{x}{13060694016})^{12} + \frac{19 !}{13 ! ( 19 - 13 ) !} \cdot 6^{6} (- 4 \frac{x}{13060694016})^{13} + \frac{19 !}{14 ! ( 19 - 14 ) !} \cdot 6^{5} (- 4 \frac{x}{13060694016})^{14} + \frac{19 !}{15 ! ( 19 - 15 ) !} \cdot 6^{4} (- 4 \frac{x}{13060694016})^{15} + \frac{19 !}{16 ! ( 19 - 16 ) !} \cdot 6^{3} (- 4 \frac{x}{13060694016})^{16} + \frac{19 !}{17 ! ( 19 - 17 ) !} \cdot 6^{2} (- 4 \frac{x}{13060694016})^{17} + \frac{19 !}{18 ! ( 19 - 18 ) !} \cdot 6^{1} (- 4 \frac{x}{13060694016})^{18} + \frac{19 !}{19 ! ( 19 - 19 ) !} \cdot 6^{0} (- 4 \frac{x}{13060694016})^{19}

\frac{19 !}{0 ! ( 19 - 0 ) !} \cdot 6^{19} (- 4 \frac{x}{13060694016})^{0}

פשט את:

6^{19}

\frac{19 !}{1 ! ( 19 - 1 ) !} \cdot 6^{18} (- 4 \frac{x}{13060694016})^{1}

פשט את:

- \frac{6 ^{18} \cdot 19 4 x}{4 13060694016}

\frac{19 !}{2 ! ( 19 - 2 ) !} \cdot 6^{17} (- 4 \frac{x}{13060694016})^{2}

פשט את:

6^{17} \cdot 171 (4 \frac{x}{13060694016})^{2}

\frac{19 !}{3 ! ( 19 - 3 ) !} \cdot 6^{16} (- 4 \frac{x}{13060694016})^{3}

פשט את:

- 6^{16} \cdot 969 (4 \frac{x}{13060694016})^{3}

\frac{19 !}{4 ! ( 19 - 4 ) !} \cdot 6^{15} (- 4 \frac{x}{13060694016})^{4}

פשט את:

139536 x

\frac{19 !}{5 ! ( 19 - 5 ) !} \cdot 6^{14} (- 4 \frac{x}{13060694016})^{5}

פשט את:

- 6^{14} \cdot 11628 (4 \frac{x}{13060694016})^{5}

\frac{19 !}{6 ! ( 19 - 6 ) !} \cdot 6^{13} (- 4 \frac{x}{13060694016})^{6}

פשט את:

6^{13} \cdot 27132 (4 \frac{x}{13060694016})^{6}

\frac{19 !}{7 ! ( 19 - 7 ) !} \cdot 6^{12} (- 4 \frac{x}{13060694016})^{7}

פשט את:

- 6^{12} \cdot 50388 (4 \frac{x}{13060694016})^{7}

\frac{19 !}{8 ! ( 19 - 8 ) !} \cdot 6^{11} (- 4 \frac{x}{13060694016})^{8}

פשט את:

\frac{2.74209 E 13 x ^{2}}{1306069401 6 ^{2}}

\frac{19 !}{9 ! ( 19 - 9 ) !} \cdot 6^{10} (- 4 \frac{x}{13060694016})^{9}

פשט את:

- 5585744406528 (4 \frac{x}{13060694016})^{9}

\frac{19 !}{10 ! ( 19 - 10 ) !} \cdot 6^{9} (- 4 \frac{x}{13060694016})^{10}

פשט את:

930957401088 (4 \frac{x}{13060694016})^{10}

\frac{19 !}{11 ! ( 19 - 11 ) !} \cdot 6^{8} (- 4 \frac{x}{13060694016})^{11}

פשט את:

- 126948736512 (4 \frac{x}{13060694016})^{11}

\frac{19 !}{12 ! ( 19 - 12 ) !} \cdot 6^{7} (- 4 \frac{x}{13060694016})^{12}

פשט את:

\frac{14105415168 x ^{3}}{1306069401 6 ^{3}}

\frac{19 !}{13 ! ( 19 - 13 ) !} \cdot 6^{6} (- 4 \frac{x}{13060694016})^{13}

פשט את:

- 1265870592 (4 \frac{x}{13060694016})^{13}

\frac{19 !}{14 ! ( 19 - 14 ) !} \cdot 6^{5} (- 4 \frac{x}{13060694016})^{14}

פשט את:

90419328 (4 \frac{x}{13060694016})^{14}

\frac{19 !}{15 ! ( 19 - 15 ) !} \cdot 6^{4} (- 4 \frac{x}{13060694016})^{15}

פשט את:

- 5023296 (4 \frac{x}{13060694016})^{15}

\frac{19 !}{16 ! ( 19 - 16 ) !} \cdot 6^{3} (- 4 \frac{x}{13060694016})^{16}

פשט את:

\frac{209304 x ^{4}}{1306069401 6 ^{4}}

\frac{19 !}{17 ! ( 19 - 17 ) !} \cdot 6^{2} (- 4 \frac{x}{13060694016})^{17}

פשט את:

- 6156 (4 \frac{x}{13060694016})^{17}

\frac{19 !}{18 ! ( 19 - 18 ) !} \cdot 6^{1} (- 4 \frac{x}{13060694016})^{18}

פשט את:

114 (4 \frac{x}{13060694016})^{18}

\frac{19 !}{19 ! ( 19 - 19 ) !} \cdot 6^{0} (- 4 \frac{x}{13060694016})^{19}

פשט את:

- (4 \frac{x}{13060694016})^{19}

= 6^{19} - \frac{6 ^{18} \cdot 19 4 x}{4 13060694016} + 6^{17} \cdot 171 (4 \frac{x}{13060694016})^{2} - 6^{16} \cdot 969 (4 \frac{x}{13060694016})^{3} + 139536 x - 6^{14} \cdot 11628 (4 \frac{x}{13060694016})^{5} + 6^{13} \cdot 27132 (4 \frac{x}{13060694016})^{6} - 6^{12} \cdot 50388 (4 \frac{x}{13060694016})^{7} + \frac{2.74209 E 13 x ^{2}}{1306069401 6 ^{2}} - 5585744406528 (4 \frac{x}{13060694016})^{9} + 930957401088 (4 \frac{x}{13060694016})^{10} - 126948736512 (4 \frac{x}{13060694016})^{11} + \frac{14105415168 x ^{3}}{1306069401 6 ^{3}} - 1265870592 (4 \frac{x}{13060694016})^{13} + 90419328 (4 \frac{x}{13060694016})^{14} - 5023296 (4 \frac{x}{13060694016})^{15} + \frac{209304 x ^{4}}{1306069401 6 ^{4}} - 6156 (4 \frac{x}{13060694016})^{17} + 114 (4 \frac{x}{13060694016})^{18} - (4 \frac{x}{13060694016})^{19}

6^{19} - \frac{6 ^{18} \cdot 19 4 x}{4 13060694016} + 6^{17} \cdot 171 (4 \frac{x}{13060694016})^{2} - 6^{16} \cdot 969 (4 \frac{x}{13060694016})^{3} + 139536 x - 6^{14} \cdot 11628 (4 \frac{x}{13060694016})^{5} + 6^{13} \cdot 27132 (4 \frac{x}{13060694016})^{6} - 6^{12} \cdot 50388 (4 \frac{x}{13060694016})^{7} + \frac{2.74209 E 13 x ^{2}}{1306069401 6 ^{2}} - 5585744406528 (4 \frac{x}{13060694016})^{9} + 930957401088 (4 \frac{x}{13060694016})^{10} - 126948736512 (4 \frac{x}{13060694016})^{11} + \frac{14105415168 x ^{3}}{1306069401 6 ^{3}} - 1265870592 (4 \frac{x}{13060694016})^{13} + 90419328 (4 \frac{x}{13060694016})^{14} - 5023296 (4 \frac{x}{13060694016})^{15} + \frac{209304 x ^{4}}{1306069401 6 ^{4}} - 6156 (4 \frac{x}{13060694016})^{17} + 114 (4 \frac{x}{13060694016})^{18} - (4 \frac{x}{13060694016})^{19}

פשט את:

6^{19} - \frac{6 ^{18} \cdot 19 4 x}{4 13060694016} + 6^{17} \cdot 171 (4 \frac{x}{13060694016})^{2} - 6^{16} \cdot 969 (4 \frac{x}{13060694016})^{3} + 139536 x - 69768 x 4 \frac{x}{13060694016} + \frac{2261 x x}{3888 6} - \frac{8398 x 4 x ^{3}}{4 1306069401 6 ^{3}} + \frac{2.74209 E 13 x ^{2}}{1306069401 6 ^{2}} - \frac{5585744406528 x ^{2} 4 \frac{x}{13060694016}}{1306069401 6 ^{2}} + \frac{3325608 6 x ^{2} x}{1306069401 6 ^{2}} - \frac{126948736512 x ^{2} 4 x ^{3}}{1306069401 6 ^{2} 4 1306069401 6 ^{3}} + \frac{14105415168 x ^{3}}{1306069401 6 ^{3}} - \frac{1265870592 x ^{3} 4 \frac{x}{13060694016}}{1306069401 6 ^{3}} + \frac{323 6 x ^{3} x}{1306069401 6 ^{3}} - \frac{5023296 x ^{3} 4 x ^{3}}{1306069401 6 ^{3} 4 1306069401 6 ^{3}} + \frac{209304 x ^{4}}{1306069401 6 ^{4}} - \frac{6156 x ^{4} 4 \frac{x}{13060694016}}{1306069401 6 ^{4}} + \frac{19 x ^{4} x}{1306069401 6 ^{4} 362797056} - \frac{x ^{4} ( 4 \frac{x}{13060694016} ) ^{3}}{1306069401 6 ^{4}}

= 6^{19} - \frac{6 ^{18} \cdot 19 4 x}{4 13060694016} + 6^{17} \cdot 171 (4 \frac{x}{13060694016})^{2} - 6^{16} \cdot 969 (4 \frac{x}{13060694016})^{3} + 139536 x - 69768 x 4 \frac{x}{13060694016} + \frac{2261 x x}{3888 6} - \frac{8398 x 4 x ^{3}}{4 1306069401 6 ^{3}} + \frac{2.74209 E 13 x ^{2}}{1306069401 6 ^{2}} - \frac{5585744406528 x ^{2} 4 \frac{x}{13060694016}}{1306069401 6 ^{2}} + \frac{3325608 6 x ^{2} x}{1306069401 6 ^{2}} - \frac{126948736512 x ^{2} 4 x ^{3}}{1306069401 6 ^{2} 4 1306069401 6 ^{3}} + \frac{14105415168 x ^{3}}{1306069401 6 ^{3}} - \frac{1265870592 x ^{3} 4 \frac{x}{13060694016}}{1306069401 6 ^{3}} + \frac{323 6 x ^{3} x}{1306069401 6 ^{3}} - \frac{5023296 x ^{3} 4 x ^{3}}{1306069401 6 ^{3} 4 1306069401 6 ^{3}} + \frac{209304 x ^{4}}{1306069401 6 ^{4}} - \frac{6156 x ^{4} 4 \frac{x}{13060694016}}{1306069401 6 ^{4}} + \frac{19 x ^{4} x}{1306069401 6 ^{4} 362797056} - \frac{x ^{4} ( 4 \frac{x}{13060694016} ) ^{3}}{1306069401 6 ^{4}}

דוגמאות פופולריות

expand (0,0,-1)*(y,x,x-1)

e x p an d (0, 0, - 1) \cdot (y, x, x - 1)

expand (1024l(c-2t-a)^2)/(405pid^4)

e x p an d \frac{1024 l ( c - 2 t - a ) ^{2}}{405 π d ^{4}}

simplify 1/3 (x-sqrt(2))(x+sqrt(2))

s im pl i f y \frac{1}{3} (x - 2) (x + 2)

expand (3x^2y+2xy+y^3)+(x^2+y^2)y'(x)

e x p an d (3 x^{2} y + 2 x y + y^{3}) + (x^{2} + y^{2}) y^{'} (x)

(d^2)/(dt^2)((x)(cos(2t)+sin(2t)+1/5 e^t))

\frac{d ^{2}}{d t ^{2}} ((x) (cos (2 t) + sin (2 t) + \frac{1}{5} e^{t}))